"Crews are working to try and get it open but I did want to advise motorists it's likely that it will sort of be on again and off again throughout the day until the snow stops falling," NZTA's Mark Owen said shortly before 8am.

"It's likely, with snow predicted throughout the day, it could remain closed for a number of hours."

MetService warned up to 10cm of snow could fall on the Rimutaka Hill Rd this morning, with the showers expected to turn to sleet or rain around noon.

An alternative route, via Ohau and Woodville, would add between three and five hours to the journey.

A KiwiRail spokesman said the Wairarapa train line was running without delays this morning.

Meanwhile, the State Highway 1 Desert Road through the Central Plateau of the North Island had opened again this morning but still had wintry conditions, NZTA warned. It had closed due to heavy snow last night.

The NZTA's Owen said that with more snow predicted to fall on the Desert Rd during the next 12 to 24 hours it was likely the road could close again tonight.

"Crews have been working hard overnight and they've got the road open but it's extreme winter driving conditions and we just advise motorists to take extra care," he told Radio NZ.

"The snow seems to have come down to quite a low level (in the North Island). It doesn't seem as heavy as we've had in other events but certainly there are a lot of roads affected, particularly a lot of local roads as well."

Snow showers were expected to become more frequent on the Desert Road this afternoon, when up to 6cm could fall, with as much as another 6cm this evening.

MetService this morning said snow was expected above about 400 metres in eastern parts of the South Island and the lower and central North Island.

Heaviest falls were expected about Taihape and inland Whanganui, along with the hills of Wellington and in the south of Wairarapa.

"The snow in Wellington and Wairarapa is expected to ease this afternoon but snow at times is likely to continue at higher levels in Whanganui and Taihape into Wednesday morning," MetService said.

"Heavy snow in these regions is likely to cause major disruptions to traffic and make driving conditions hazardous, especially about higher mountain roads and passes. Strong southerlies along with the cold temperatures will make the wind feel bitterly cold. Farmers are advised that stock may need shelter."